1
JEE Main 2022 (Online) 26th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$f(x) = \left\{ {\matrix{ {{x^3} - {x^2} + 10x - 7,} & {x \le 1} \cr { - 2x + {{\log }_2}({b^2} - 4),} & {x > 1} \cr } } \right.$$.

Then the set of all values of b, for which f(x) has maximum value at x = 1, is :

A
($$-$$6, $$-$$2)
B
(2, 6)
C
$$[ - 6, - 2) \cup (2,6]$$
D
$$\left[ {-\sqrt 6 , - 2} \right) \cup \left( {2,\sqrt 6 } \right]$$
2
JEE Main 2022 (Online) 26th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

If $$a = \mathop {\lim }\limits_{n \to \infty } \sum\limits_{k = 1}^n {{{2n} \over {{n^2} + {k^2}}}} $$ and $$f(x) = \sqrt {{{1 - \cos x} \over {1 + \cos x}}} $$, $$x \in (0,1)$$, then :

A
$$2\sqrt 2 f\left( {{a \over 2}} \right) = f'\left( {{a \over 2}} \right)$$
B
$$f\left( {{a \over 2}} \right)f'\left( {{a \over 2}} \right) = \sqrt 2 $$
C
$$\sqrt 2 f\left( {{a \over 2}} \right) = f'\left( {{a \over 2}} \right)$$
D
$$f\left( {{a \over 2}} \right) = \sqrt 2 f'\left( {{a \over 2}} \right)$$
3
JEE Main 2022 (Online) 26th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $${{dy} \over {dx}} + 2y\tan x = \sin x,\,0 < x < {\pi \over 2}$$ and $$y\left( {{\pi \over 3}} \right) = 0$$, then the maximum value of $$y(x)$$ is :

A
$${1 \over 8}$$
B
$${3 \over 4}$$
C
$${1 \over 4}$$
D
$${3 \over 8}$$
4
JEE Main 2022 (Online) 26th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A point $$P$$ moves so that the sum of squares of its distances from the points $$(1,2)$$ and $$(-2,1)$$ is 14. Let $$f(x, y)=0$$ be the locus of $$\mathrm{P}$$, which intersects the $$x$$-axis at the points $$\mathrm{A}$$, $$\mathrm{B}$$ and the $$y$$-axis at the points C, D. Then the area of the quadrilateral ACBD is equal to :

A
$${9 \over 2}$$
B
$${{3\sqrt {17} } \over 2}$$
C
$${{3\sqrt {17} } \over 4}$$
D
9
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